The present invention relates to a method for measuring the concentration of NOx in a gas to be measured (hereinafter referred to as a measurement gas), such as exhaust gas emitted from combustion equipment or an internal combustion engine, as well as to an NOx concentration sensor.
Also, the present invention relates to an NOx concentration sensor for measuring the concentration of NOx in exhaust gas emitted from an internal combustion engine used in transportation equipment such as an automobile, ship, or an airplane, or industrial equipment such as a boiler, as well as to an apparatus and a method for measuring NOx concentration.
Conventionally, a method has been proposed for measuring NOx concentration using an NOx concentration sensor including two measurement spaces and two oxygen ion pumping cells (hereinafter referred to as pumping cells). The conventional method includes the steps of: pumping out oxygen from one measurement space by means of a first pumping cell to an extent so as not to cause dissociation of NO; causing NO to completely dissociate in the other measurement space by means of a second pumping cell; and determining NOx concentration based on a pumping current induced by oxygen ions generated by dissociation of NO.
For example, Japanese Patent Application Laid-Open (Kokai) No. 2-1543 proposes a method for measuring the concentration of NOx, typically nitrogen monoxide (NO), contained in exhaust gas, using an NOx concentration sensor composed of two measurement spaces, each of which is equipped with a pumping cell. The method includes the steps of: pumping out only oxygen from one measurement space to an extent so as not to cause dissociation of NO; measuring a current, Ip1, flowing through a pumping cell (hereinafter referred to as a pumping current) associated with the measurement space; causing O2 and NO to dissociate in the second measurement space; pumping out, from the second measurement space, oxygen generated by dissociation of O2 and NO; measuring a pumping current, Ip2, flowing through the second pumping cell; and determining NOx concentration based on the difference between the pumping currents (Ip2xe2x88x92Ip1).
Japanese Patent Application Laid-Open (Kokai) No. 2 122255 proposes a method for measuring the concentration of a certain gas component contained in a mixed gas which contains an oxygen compound other than the gas component to be measured. The method includes the steps of: causing dissociation of the oxygen compound having a dissociation voltage lower than that of the gas component to be measured, by applying a certain fixed voltage (which does not cause dissociation of the gas component to be measured) to a first pumping cell; pumping out oxygen generated by dissociation of the oxygen compound; causing dissociation of the gas component to be measured by applying a certain voltage to a second pumping cell; detecting the amount of oxygen generated by dissociation of the gas component to be measured in terms of a second pumping current, Ip2; and determining the concentration of the gas component to be measured based on the second pumping current Ip2.
Japanese Patent Application Laid-Open (Kokai) No. 8 271476 proposes an improvement in the above-described method for measuring NOx concentration. The method includes the steps of: eliminating excess oxygen from a first space by controlling the amount of oxygen contained in the first space so as not to substantially affect the measurement of NOx concentration and so as not to cause substantial dissociation of NO; causing dissociation of NO in a second space; and determining NOx concentration based on a pumping current, Ip2, induced by oxygen generated by dissociation of NO.
The above-described methods have been developed in order to measure the concentration of NOx, for example, in an automobile exhaust gas. However, recently, there has arisen a need for measuring the concentration of NOx in a catalytically purified exhaust gas, in order to verify the purification performance of an exhaust gas purification catalyst. In this case, the accuracy required for measuring NOx concentration is not greater than xc2x1 several tens of ppm with respect to several hundreds of ppm in NOx concentration. The above-described methods fail to sufficiently satisfy this accuracy requirement and thus there is a need for further improvement.
The method for measuring NOx concentration using the aforementioned NOx concentration sensor significantly depends on oxygen concentration and temperature, and therefore it is difficult to accurately measure the NOx concentration.
In the NOx sensor proposed in the above-mentioned Japanese Patent Application Laid-Open (Kokai) No. 2-1543, the first pumping current Ip1 is relatively strong. Thus, the differential pumping current (Ip2xe2x88x92Ip1) is considerably influenced by variation of the first pumping current Ip1. Therefore, due to variation among sensors and temperature, measurement accuracy is impaired.
In the above method described in Japanese Patent Application Laid-Open (Kokai) No. 8-271476, oxygen in the first space is held at a partial pressure of 10xe2x88x924 to 10xe2x88x926 atm so as not to cause dissociation of NO within the first space. Thus, a considerable amount of oxygen is introduced into the second space. The relatively large amount of oxygen present within the second space hinders sufficient dissociation of NO within the second space. Also, the absolute quantity of variation in the oxygen concentration of gas introduced into the second space increases. As a result, an electric signal issued by the second pumping cell includes a measurement error, thus causing a failure to attain the required measurement accuracy.
The present invention has been achieved in view of the above problems of the prior art. It is therefore an object of the present invention to provide a method capable of accurately measuring NOx concentration, as well as an NOx concentration sensor capable of accurately measuring NOx concentration.
Nitrogen monoxide (NO) is dominant among NOx contained, for example, in an automobile exhaust gas. In other words, the content of NOx species other than NO, that is, the content of N2O and NO2, is very low. Therefore, the following description relates to the measurement of NO concentration. The term xe2x80x9cNOx concentrationxe2x80x9d substantially means xe2x80x9cNO concentrationxe2x80x9d.
The above object of the present invention has been achieved by providing a two-serial-space NOx concentration sensor comprising a measurement gas space (ambient atmosphere to be measured) in series communication with a first internal space a second internal space. A measurement gas is introduced from the measurement gas space into the first space and then into the second space.
In the NOx concentration sensor, by activating a first pumping cell, a portion of oxygen (O2) and nitrogen monoxide (NO) contained in the first space dissociates to generate oxygen ions (O2xe2x88x92). The thus-generated oxygen ions are transferred (pumped out) into the measurement gas space. By contrast, oxygen can also be pumped into the first space from the measurement gas space. By activating a second pumping cell, residual O2 and NO contained in gas diffusing within the second space dissociate to generate oxygen ions, which are also removed by pumping. The first pumping cell and the second pumping cell may each comprise a solid electrolyte substrate and a pair of porous electrodes disposed on opposite sides or a single side of the substrate. By applying a predetermined voltage between the porous electrodes, oxygen can be transferred from one of the porous electrodes to the other.
To achieve the above object, a first mode of a first aspect of the present invention provides a method for measuring NOx concentration using a two-serial-space NOx concentration sensor. The sensor includes a first pumping cell and a second pumping cell each comprising a solid electrolyte. In the sensor, a measurement gas space, a first space, and a second space communicate in series with each other. The method comprises the steps of: pumping out oxygen from the first space into, for example, the measurement gas space, or pumping oxygen into the first space from, for example, the measurement gas space by action of the first pumping cell so that the oxygen concentration in the vicinity of a gas inlet of the second space becomes such that a portion of NO in the first space dissociates; dissociating residual NO and O2 in gas introduced into the second space from the first space by action of the second pumping cell; pumping out oxygen ions generated by dissociation of NO and O2 from the second space by action of the second pumping cell; and determining the concentration of NOx in the measurement gas based on signals (for example, pumping currents) issued from the first and second pumping cells.
Problems Solved by the Invention
FIG. 1 shows an NOx concentration sensor in accordance with the present invention. The measurement gas is introduced into the first space from the measurement gas space. The first pumping cell is operated so that the oxygen concentration in the vicinity of the gas inlet of the second space becomes such that a portion of NO in the first space dissociates. In the present invention, the degree of dissociation of NO in the first space is represented by the dissociation percentage xcex1 (%).
As a result of the above-mentioned control of oxygen concentration in the vicinity of the gas inlet of the second space, the oxygen concentration of the second space decreases, thereby eliminating a hindrance to dissociation of NO which would otherwise result from the presence of oxygen. As a result, NO dissociates sufficiently by action of the second pumping cell, so that a signal associated with the dissociation of NO and issuing from the second pumping cell can be obtained with good sensitivity.
In the present invention, the oxygen concentration of the measurement gas introduced into the second space from the first space is decreased such that a portion of No in the first space dissociates. Accordingly, the magnitude of the Ip2offset signal associated with oxygen concentration and issuing from the second pumping cell becomes low. Furthermore, the extent of variation in Ip2offset becomes small. Thus, Ip2offset less strongly affects the signal Ip2-Ip2offset, associated with the quantity of NO dissociated and issuing from the second pumping cell, to thereby provide improved accuracy in measuring NO concentration.
In the present invention, NO in the measurement gas dissociates within the first space to a predetermined degree (a predetermined dissociation percentage xcex1). Furthermore, residual NO dissociates within the second space. Accordingly, as described below in relation to an eighth mode of the first aspect of the invention, the concentration of NO in the measurement gas can be determined based on the NO dissociation percentage in the first space and the quantity of NO dissociated in the second space.
Accordingly, the concentration of NO in the measurement gas can be determined based on a signal (for example, the first pumping current) associated with the dissociation of NO within the first space and issuing from the first pumping cell and a signal (for example, the second pumping current) associated with the dissociation of NO within the second space and issuing from the second pumping cell.
According to a second mode of the first aspect of the present invention, in the method for measuring NOx concentration as described in the first mode of the first aspect of the invention, the first space of the NOx concentration sensor communicates with the measurement gas space via a first diffusion resistance element, and the first space and the second space communicate via a second diffusion resistance element.
In the second mode of the first aspect of the invention, the measurement gas space and the first space communicate via the first diffusion resistance element. Thus, the measurement gas space is diffusion-controlled by the first diffusion resistance element. Thus, the measurement gas introduced into the first space from the measurement gas space is diffusion-controlled by the first diffusion resistance element. Through this diffusion control, the quantities of oxygen and NO introduced into the first space are limited. Accordingly, even when a voltage is applied between the electrodes of the first pumping cell, the first pumping current does not flow in excess of a certain limiting value.
Similarly, the first space and the second space communicate via the second diffusion resistance element. Accordingly, the measurement gas introduced into the second space is diffusion-controlled by the second diffusion resistance element. Through this diffusion control, the quantities of oxygen and NO introduced into the first space are limited. Accordingly, even when a voltage is applied between the electrodes of the second pumping cell, the second pumping current does not flow in excess of a certain limiting value.
The above-mentioned sensor having diffusion resistance elements is called a limit-current-type sensor and can obtain the concentration of oxygen or NO contained in a measurement gas stably and accurately. This is because a limit current can be obtained according to the concentration of oxygen or NO in the measurement gas.
According to a third mode of the first aspect of the present invention, in the method for measuring NOx concentration as described in the first or second mode of the first aspect of the invention, an oxygen-concentration-measuring cell for detecting the concentration of oxygen in gas introduced into the second space of the NOx concentration sensor is disposed in the vicinity of the gas inlet of the second space.
The third mode of the first aspect of the invention provides a method for detecting oxygen concentration in the vicinity of the gas inlet of the second space. Specifically, the oxygen-concentration-measuring cell is disposed in the vicinity of the gas inlet of the second space.
By detecting the oxygen concentration in the vicinity of the gas inlet of the second space by means of the oxygen-concentration-measuring cell, even when the distribution of oxygen concentration within the first space varies greatly, the oxygen concentration of the measurement gas introduced into the second space can be accurately controlled.
The oxygen-concentration-measuring cell can assume the form of an oxygen concentration cell, which generates an electromotive force according to an oxygen concentration differential. The oxygen-concentration-measuring cell may be composed of, for example, a solid electrolyte substrate and a pair of porous electrodes disposed on opposite sides of the substrate. In this case, one of the electrodes is disposed so as to contact the measurement gas, whereas the other electrode is disposed so as to contact a reference gas. As a result, an electromotive force is generated depending on the oxygen concentration differential between the electrodes. Based on the generated electromotive force (Vsm), the oxygen concentration on the measurement gas side of the cell can be determined.
According to a fourth mode of the first aspect of the present invention, in the method for measuring NOx concentration as described in any of the first through third modes of the first aspect of the invention, the first pumping cell is controlled based on a signal issuing from the oxygen-concentration-measuring cell for detecting oxygen concentration in the vicinity of the gas inlet of the second space of the NOx concentration sensor.
The fourth mode of the first aspect of the invention provides a method for controlling the first pumping cell. Specifically, the first pumping cell is controlled based on a signal issuing from the oxygen-concentration-measuring cell.
As mentioned above in relation to the third mode of the first aspect of the invention, a signal (for example, voltage Vsm) issuing from the oxygen-concentration-measuring cell indicates the oxygen concentration as detected in the vicinity of the gas inlet of the second space. Thus, the first pumping cell is controlled such that Vsm approaches a predetermined target value, namely, such that Vsm achieves a target voltage Vs, thereby controlling the quantity of oxygen that is pumped out from or pumped into the first space. As a result, oxygen concentration in the vicinity of the gas inlet of the second space can be controlled to a desired value, which corresponds to the target voltage Vs.
According to a fifth mode of the first aspect of the present invention, in the method for measuring NOx concentration as described in any of the first through fourth modes of the first aspect of the invention, a target value of the oxygen concentration in the vicinity of the gas inlet of the second space is set to a value not higher than 2xc3x9710xe2x88x927 atm in terms of oxygen partial pressure.
The fifth mode of the first aspect of the invention specifies a target value of the oxygen concentration in the vicinity of the gas inlet of the second space.
Specifically, the target oxygen concentration in the vicinity of the gas inlet of the second space is set to a partial pressure of oxygen of not higher than 2xc3x9710xe2x88x927 atm, but higher than 2xc3x9710xe2x88x9210 atm , which is a sufficiently low level to cause partial dissociation of NO in the first space.
Accordingly, as described above in relation to the first mode of the first aspect of the invention, the oxygen concentration of the second space is sufficiently decreased, thereby decreasing an offset component of the second pumping current and thus enabling accurate measurement of NO concentration. The above-mentioned target oxygen concentration is more preferably set to a value of from 2xc3x9710xe2x88x928 to 2xc3x9710xe2x88x929 atm in terms of an oxygen partial pressure.
According to a sixth mode of the first aspect of the present invention, in the method for measuring NOx concentration as described in any of the first through fifth modes of the first aspect of the invention, the NO dissociation percentage in the first space is not lower than 0.5%.
The sixth mode of the first aspect of the invention specifies, in terms of the degree of dissociation of NO (dissociation percentage xcex1), that the oxygen concentration in the vicinity of the gas inlet of the second space is decreased such that a portion of NO in the first space dissociates.
Specifically, oxygen concentration in the vicinity of the gas inlet of the second space is decreased such that the NO dissociation percentage in the first space becomes not lower than 0.5%. As a result, as described above in relation to the first mode of the first aspect of the invention, the oxygen concentration of the second space is decreased to thereby improve accuracy in measuring NO concentration.
According to a seventh mode of the first aspect of the present invention, in the method for measuring NOx concentration as described in any of the first through sixth modes of the first aspect of the invention, the NO dissociation percentage in the first space is 1% to 50%.
The seventh mode of the first aspect of the invention specifies a more preferable dissociation percentage range. Specifically, when the NO dissociation percentage is not lower than 1%, as described above in relation to the first mode of the first aspect of the invention, the oxygen concentration of the second space is further decreased to thereby improve accuracy in measuring NO concentration.
When the NO dissociation percentage is in excess of 50%, an offset component of the second pumping current is limited to a low level; however, the NO dissociation percentage varies greatly with a variation in the oxygen concentration and temperature of the measurement gas space. Thus, measurement accuracy deteriorates greatly where environmental conditions vary significantly. More preferably, the NO dissociation percentage is 2% to 20%.
According to an eighth mode of the first aspect of the present invention, in the method for measuring NOx concentration as described in any of the first through seventh modes of the first aspect of the invention, the concentration of NOx in the measurement gas is calculated based on signals corresponding to the NO dissociation percentage in the first space and the quantity of NO dissociated in the second space.
The eighth mode of the first aspect of the invention specifies a method for determining the concentration of NOx in the measurement gas. The NOx concentration is calculated based on a signal issuing from the first pumping cell (for example, the first pumping current) and a signal issuing from the second pumping cell (for example, the second pumping current).
The operation of the first pumping cell causes NO in the first space to dissociate to a certain degree (at a certain dissociation percentage xcex1). Accordingly, a signal issuing from the first pumping cell corresponds to the oxygen concentration of the measurement gas and the NO dissociation percentage in the first space. Also, operation of the second pumping cell causes residual NO, namely, NO which has not dissociated in the first space and which has been introduced into the second space, to dissociate in the second space. Accordingly, a signal issuing from the second pumping cell corresponds to the quantity of NO dissociated in the second space and the quantity of oxygen introduced into the second space.
When the NOx concentration of the measurement gas is calculated based on the above-mentioned two signals, the effect of oxygen concentration must be eliminated. For example, because the second pumping current includes an offset current induced by oxygen concentration, the offset current is preferably eliminated, as described below.
According to a ninth mode of the first aspect of the present invention, in a method for measuring NOx concentration as described in the eighth mode of the first aspect of the invention, the concentration of NOx in the measurement gas is calculated according to the following calculational expression (A1):.
NOx concentration=(Ip2xe2x88x92Ip2offset)xc3x97A/(1xe2x88x92xcex1/100) (A1)
where
xcex1: NO dissociation percentage in the first space (%),
A: coefficient for converting a current signal corresponding to NOx concentration to an NOx concentration,
Ip2: current flowing through the second pumping cell,
Ip2offset: offset component of current flowing through the second pumping cell, and
NOx concentration: concentration of NOx contained in the measurement gas.
The calculational expression Al is described in detail below.
According to the present invention, the measurement gas is introduced into the first space to form a new gas which then enters the second space via a gas diffusion resistance that separates the first and second space. The operation of the first pumping cell dissociates O2 to a certain oxygen partial pressure level and also causes NO in the first space to partially dissociate to a certain degree (at a certain dissociation percentage xcex1).
Operation of the second pumping cell causes the residual NO, namely, NO which has not dissociated in the first space and which has been introduced into the second space, to dissociate in the second space. Accordingly, NO concentration can be detected based on the state of dissociation of NO in the first and second spaces.
Specifically, because current flowing through the second pumping cell (the second pumping current Ip2) corresponds to the quantity of NO and the quantity of O2 dissociated in the second space, the offset current Ip2offset, which corresponds to the quantity of O2 dissociated in the second space, is desirably eliminated from the second pumping current Ip2. The resulting difference, Ip2xe2x88x92Ip2offset, corresponds to the quantity of NO dissociated in the second space.
When the NO concentration of the measurement gas is taken as 1, the NO concentration of the measurement gas introduced into the second space can be represented by xe2x80x9c1xcex1/100.xe2x80x9d If all of the NO introduced into the second space dissociates, then a current corresponding to the NO concentration of the measurement gas is represented by xe2x80x9c(Ip2xe2x88x92Ip2offset)/(1xe2x88x92xcex1/100).xe2x80x9d
Accordingly, by multiplying the current (Ip2xe2x88x92Ip2offset)/(1xe2x88x92xcex1/100) by a predetermined coefficient (a coefficient for converting current to NO concentration) A, the concentration of NO in the measurement gas space is obtained.
As will be later described in detail, the offset current Ip2offset appearing in the equation A1 is obtained from the first pumping current Ip1. This is because the Ip2offset can be determined by a relation (or map) pre-measured or rather predetermined with the electromotive force cell voltage Vs that represents an oxygen partial pressure level at an inlet of the second passage (or rather at an outlet of the first passage), and further because the voltage Vs can also act as a parameter functioning between the first pumping current Ip1 and the oxygen concentration level of a measurement gas of interest entering the first passage.
According to a tenth mode of the first aspect of the present invention, the method for measuring NOx concentration as described in the ninth mode of the first aspect of the invention employs an NOx concentration sensor in which the first pumping cell is controlled such that a signal issuing from the oxygen-concentration-measuring cell for detecting oxygen concentration in the vicinity of the gas inlet of the second space assumes a target value. The method comprises the steps of: calculating the concentration of oxygen in the measurement gas using a map of a previously measured relationship between current flowing through the first pumping cell and the concentration of oxygen in the measurement gas while taking the target value as a parameter; and calculating Ip2offset using a map of a previously measured relationship between Ip2offset and the concentration of oxygen in the measurement gas while taking the target value as a parameter.
The tenth mode of the first aspect of the invention provides a more specific method according to the ninth mode of the first aspect of the invention.
In order to calculate the concentration of oxygen in the measurement gas, a map showing the relationship among the target value (target voltage Vs for the oxygen-concentration-measuring cell), current flowing through the first pumping cell (the first pumping current Ip1), and the oxygen concentration of the measurement gas is experimentally prepared in advance, for example, as shown in FIG. 2. The concentration of oxygen in the measurement gas is obtained using this map, and is based on a measured value of Ip1 and a predetermined target value of Vs.
Also, for example, as shown in FIG. 3, a map showing the relationship among the target value (Vs), the offset current Ip2offset, and the oxygen concentration of the measurement gas is experimentally prepared in advance. The offset current Ip2offset is obtained using this map, and is based on a predetermined target value of Vs and the above-obtained oxygen concentration.
The offset current Ip2offset for use in the expression A1 is thus obtained. The maps shown in FIGS. 2 and 3 are in the form of a graph representing the relationship between oxygen concentration and a pumping current, but are not limited thereto. Alternatively, the maps may assume, for example, the form of an ordinary matrix table.
According to an eleventh mode of the first aspect of the present invention, the method for measuring NOx concentration as described in the ninth mode of the first aspect of the invention employs an NOx concentration sensor in which the first pumping cell is controlled such that a signal issuing from the oxygen-concentration-measuring cell for detecting oxygen concentration in the vicinity of the gas inlet of the second space assumes a target value. The method comprises the steps of: calculating the concentration of oxygen in the measurement gas using a map of a previously measured relationship between current flowing through the first pumping cell and the concentration of oxygen in the measurement gas while taking the target value as a parameter; and calculating A/(1xe2x88x92xcex1/100) (hereinafter referred to as gain) using a map of a previously measured relationship between gain and the concentration of oxygen in the measurement gas while taking the target value as a parameter.
The eleventh mode of the first aspect of the invention provides a more specific method according to the ninth mode of the first aspect of the invention.
As described above in relation to the tenth mode of the first aspect of the invention, the concentration of oxygen in the measurement gas is calculated based on the first pumping current Ip1 and by using, for example, the map shown in FIG. 2. As shown in FIG. 4, a map is experimentally prepared in advance showing the relationship among the target oxygen concentration (the target voltage Vs for the oxygen-concentration-measuring cell), gain and the concentration of oxygen in the measurement gas. The gain is obtained using this map, and is based on Vs and the above-obtained oxygen concentration. Notably, the map shown in FIG. 4 may also assume the form of an ordinary matrix table as in the case of other similar maps.
The gain is thus obtained. Also, the offset current Ip2offset is obtained according to the aforementioned tenth mode of the first aspect of the invention. Furthermore, the second pumping current Ip2 is obtained by actual measurement. By substituting these values into the expression A1, the NO concentration can be obtained, or the substantial NOx concentration of the measurement gas can be obtained.
According to a first mode of a second aspect of the present invention, an NOx concentration sensor is provided which is a two-serial-space-type NOx concentration sensor comprising a first space, a second space, a first diffusion resistance element and a second diffusion resistance element. The first space is partially defined by a first pumping cell and an oxygen-concentration-measuring cell, each comprising a solid electrolyte layer and a pair of electrodes. The second space is partially defined by a second pumping cell comprising a solid electrolyte layer and a pair of electrodes. The first diffusion resistance element establishes communication between the first space and a measurement gas space. The second diffusion resistance element establishes communication between the first space and the second space. The oxygen-concentration-measuring cell is disposed in the vicinity of the second diffusion resistance element, and the sensor further comprises a measuring section (which can comprise a circuit) for measuring a first pumping current flowing through the first pumping cell, a measuring section (which can comprise a circuit) for measuring a second pumping current flowing through the second pumping cell, and a calculation section (which can comprise a circuit and/or a microprocessor and associated memory) for calculating the concentration of NOx in the measurement gas based on the first pumping current and the second pumping current.
The first mode of the second aspect of the invention specifies the structure of the NOx concentration sensor.
In the NOx concentration sensor, oxygen concentration in the vicinity of the gas inlet of the second space is measured by the oxygen-concentration-measuring cell disposed in the vicinity of the second diffusion resistance element. The first pumping cell is operated such that the thus-measured oxygen concentration assumes a predetermined value (namely, such that a portion of NO in the first space dissociates). At this time, the first pumping current and the second pumping current are measured. Based on the measured currents, the concentration of NO in the measurement gas is determined, as described in detail below.
According to a second mode of the second aspect of the present invention, in the NOx concentration sensor as described in the first mode of the second aspect of the invention, oxygen is pumped out from or pumped into the first space by means of the first pumping cell so that the oxygen concentration in the vicinity of the gas inlet of the second space becomes such that a portion of the NO contained in the first space dissociates.
The second mode of the second aspect of the invention specifies the function of the first pumping cell. By applying a voltage between the electrodes of the first pumping cell, the first pumping cell is activated so as to pump out oxygen from or pump oxygen into the first space. As a result, the oxygen concentration in the vicinity of the gas inlet of the second space is regulated such that a portion of the NO contained in the first space dissociates.
According to a third mode of the second aspect of the present invention, in the NOx concentration sensor as described in the first or second mode of the second aspect of the invention, the calculation section calculates the concentration of NOx in the measurement gas according to the following calculational expression A1:
NOx concentration=(Ip2xe2x88x92Ip2offset)xc3x97A/(1xe2x88x92xcex1/100) (A1) where
xcex1: NO dissociation percentage in the first space (%),
A: coefficient for converting a current signal corresponding to NOx concentration to an NOx concentration,
Ip2: current flowing through the second pumping cell,
Ip2offset: offset component of current flowing through the second pumping cell, and
NOx concentration: concentration of NOx in the measurement gas.
The third mode of the second aspect of the invention provides an NOx concentration sensor for implementing the method of the ninth mode of the first aspect of the invention.
Accordingly, the expression A1 has the same meaning as in the ninth mode of the first aspect of the invention.
Specifically, because the quantity xe2x80x9cIp2xe2x88x92Ip2offsetxe2x80x9d corresponds to a signal which, in turn, corresponds to the quantity of NO dissociated in the second space, a current corresponding to the concentration of NO in the measurement gas is represented by (Ip2xe2x88x92Ip2offset)/(1xe2x88x92xcex1/100). Accordingly, by multiplying the current (Ip2xe2x88x92Ip2offset)/(1xe2x88x92xcex1/100) by the conversion coefficient A, the concentration of NO in the measurement gas can be obtained.
According to a fourth mode of the second aspect of the present invention, the NOx concentration sensor as described in the third mode of the second aspect of the invention, in which the first pumping cell is controlled such that a signal issuing from the oxygen-concentration-measuring cell for detecting oxygen concentration in the vicinity of the gas inlet of the second space assumes a target value, further comprises an oxygen concentration calculation section (which may comprise a circuit and/or a microprocessor and associated memory) and an Ip2offset calculation section (which may comprise a circuit and/or a microprocessor and associated memory). The oxygen concentration calculation section calculates the concentration of oxygen in the measurement gas using a map which shows a previously measured relationship between current flowing through the first pumping cell and the concentration of oxygen in the measurement gas while taking the target value as a parameter, that is, for a certain target value. The Ip2offset calculation section calculates Ip2offset using a map which shows the previously measured relationship between Ip2offset and the concentration of oxygen in the measurement gas while taking the target value as a map parameter.
The fourth mode of the second aspect of the invention provides an NOx concentration sensor for implementing the method of the tenth mode of the first aspect of the invention.
As in the case of the tenth mode of the first aspect of the invention, the concentration of oxygen in the measurement gas is obtained using the map of FIG. 2. Based on the thus-obtained oxygen concentration, the offset current Ip2offset can be obtained using the map of FIG. 3.
According to a fifth mode of the second aspect of the present invention, the NOx concentration sensor as described in the third or fourth mode of the second aspect of the invention, in which the first pumping cell is controlled such that a signal issuing from the oxygen-concentration-measuring cell for detecting oxygen concentration in the vicinity of the gas inlet of the second space assumes a target value, further comprises an oxygen concentration calculation section and a gain calculation section (which may comprise a circuit and/or a microprocessor and associated memory). The oxygen concentration calculation section calculates the concentration of oxygen contained in the measurement gas using a map which shows a previously measured relationship between current flowing through the first pumping cell and the concentration of oxygen in the measurement gas while taking the target value as a parameter. The gain calculation section calculates A/(1xe2x88x92xcex1/100) (gain) using a map which shows a previously measured relationship between the gain and the concentration of oxygen in the measurement gas while taking the target value as a parameter.
The fifth mode of the second aspect of the invention provides an NOx concentration sensor for implementing the method of the eleventh mode of the first aspect of the invention.
As in the case of the eleventh mode of the first aspect of the invention, the concentration of oxygen in the measurement gas is obtained using the map of FIG. 2. Based on the thus-obtained oxygen concentration, the gain can be obtained using the map of FIG. 4.
In measuring NOx concentration using the NOx concentration sensor described above, the sensor is preferably controlled to a predetermined temperature of 550 to 900xc2x0 C. by disposing one or more heaters on a single side or on opposite sides of the sensor.
As shown in FIG. 5, the NO dissociation percentage in the first space varies with the temperature of the sensor (element temperature). Therefore, the sensor is preferably used within a temperature range such that the NO dissociation percentage does not vary greatly. In another aspect for providing accurate NOx measurement, it is important to maintain a temperature drift of the sensor within xc2x15xc2x0 C., preferably xc2x12.5xc2x0 C., more preferably xc2x11xc2x0 C. This is because the sensor temperature drift varies the NO dissociation percentage and in turn affects the measurement accuracy.
In the above description of the present invention, the dissociation of NO and oxygen means the separation of NO and oxygen into simpler constituents. For example, as shown in the formulae below, nitrogen monoxide (NO) dissociates into nitrogen (molecular nitrogen N2) and oxygen (molecular oxygen O2) , and oxygen (molecular oxygen O2) dissociates into oxygen ions (O2xe2x88x92).
2NOxe2x86x92N2+O2
O2+4exe2x86x922O2xe2x88x92
A first mode of a third aspect of the present invention has the following features. A measurement gas including O2 and NOx diffuses into a first passage, which faces a first pumping cell, and then diffuses into a second passage, which faces a second pumping cell. The first pumping cell causes a portion of O2 and NO contained in the gas which has diffused into the first passage to dissociate, thereby controlling the concentration of oxygen in the gas contacting the second pumping cell to as low a level as possible. The second pumping cell causes residual NO contained in the gas which has diffused into the second passage to dissociate.
The preferable range of the oxygen concentration of the gas detected at the inlet of the second passage, said gas then contacting with the second pump cell electrode, is from 2xc3x9710xe2x88x927 to 2xc3x9710xe2x88x9210 atm and more preferably from 2xc3x9710xe2x88x928 to 2xc3x9710xe2x88x929 atm defined by oxygen partial pressure, according to the invention. The range is calculated from the oxygen concentration cell voltage Vs, based on the known Nernst equation. In this range of the oxygen concentration, the improved accuracy of NOx measurement is attained because of a decomposition rate or dissociation percentage a of NO in the first passage where the first pumping cell is located can become constantly stable even if a substantial decomposition of No occurs in the first passage.
In the case that the oxygen concentration measuring cell (EMF cell) has an oxygen reference electrode communicating with the atmospheric air having an oxygen partial pressure of about 2xc3x9710xe2x88x921 atm, the Vsm value measured at the oxygen concentration detection electrode of the cell corresponding to the above oxygen concentration range (of 2xc3x9710xe2x88x927 to 2xc3x9710xe2x88x9210 atm.) is from 300 mV to 450 mV. When the oxygen concentration cell has the oxygen reference electrode communicating with a self-made oxygen reference atmosphere having about 2xc3x9710xe2x88x921 atm. (as the case for the embodiment later explained), the corresponding Vsm is from 350 mV to 500 mV, measuring about 50 mV higher than the above range.
A second mode of the third aspect of the present invention includes means for correcting the measurement of NOx concentration to take into account a variation in the NO dissociation percentage in the first passage with a change in the concentration of oxygen in the measurement gas. Preferably, the term xcex94Ip2=(Ip2xe2x88x92Ip2offset) is multiplied by a predetermined coefficient, which is a function of the NO dissociation percentage in the first passage. The measurement of NOx concentration can be further corrected for other factors by multiplying the term xcex94Ip2 by another coefficient. The coefficient is experimentally obtained in advance and is selected according to Ip1 and/or Ip2, thereby further improving accuracy in measuring NOx concentration.
A third mode of the third aspect of the present invention includes means for correcting the measurement of NOx concentration to take into account a variation in the ratio between the concentration of NOx in the measurement gas and the concentration of NOx in the gas diffusing into the second passage caused by control of oxygen concentration by said first pumping cell.
A fourth mode of the third aspect of the present invention includes means for correcting the measurement of NOx concentration to take into account a variation in the ratio between the concentration of NOx in the measurement gas and the concentration of NOx in the gas diffusing into the second passage with a change in NO dissociation percentage in the first passage.
A first mode of a fourth aspect of the present invention provides an NOx concentration sensor comprising a first passage, a second passage, an oxygen-concentration-measuring cell, a first pumping cell and a second pumping cell. A measurement gas diffuses into the first passage via a first diffusion resistance element. In the first passage, O2 and NO are partially dissociated. Gas leaving the first passage diffuses into the second passage via a second diffusion resistance element facing a downstream end portion of the first passage. In the second passage, residual NO and O2 in the gas introduced from the first passage are dissociated. The oxygen-concentration-measuring cell has an electrode which is disposed downstream of the first passage and on the inlet side of or facing the second diffusion resistance element. The oxygen-concentration-measuring cell (EMF cell) measures the oxygen partial pressure by voltage developed across the oxygen concentration detection electrodes as described, for example, in U.S. Pat. No. 4,272,329 incorporated herein by reference. The first pumping cell has an electrode facing the first passage. By applying a voltage to the electrode of the first pumping cell based on the electromotive force output from the oxygen-concentration-measuring cell, the first pumping cell causes a portion of O2 and NO in the first passage to dissociate. A current (first pumping current) induced by oxygen ions generated by dissociation of O2 and NO flows through the first pumping cell. The second pumping cell has an electrode facing the second passage. By applying a voltage to the electrode of the second pumping cell, the second pumping cell causes residual O2 and NO contained in the gas which has diffused into the second passage to dissociate. A current (second pumping current) induced by oxygen ions generated by dissociation of residual O2 and NO flows through the second pumping cell.
According to a second mode of the fourth aspect of the invention, the concentration of NOx in the measurement gas is obtained based on the first pumping current flowing through the first pumping cell and the second pumping current flowing through the second pumping cell. The first pumping current includes a current component induced by oxygen ions generated by the dissociation of NO in the first passage. The second pumping current includes a current component induced by oxygen ions generated by the dissociation of NO in the second passage.
According to a third mode of the fourth aspect of the invention, the electrode of the first pumping cell extends along a gas flow within the first passage and on a solid electrolyte layer which constitutes the first pumping cell.
According to a fourth mode of the fourth aspect of the invention, the electrode of the oxygen-concentration-measuring cell is formed on a solid electrolyte layer which constitutes the oxygen-concentration-measuring cell, in such manner as to be located downstream of the first passage and in the vicinity of an inlet to or facing the second diffusion resistance element.
A first mode of a fifth aspect of the present invention has the following features. A measurement gas including O2 and NOx diffuses into a first passage. A portion of the O2 and NO in the gas which has diffused into the first passage is dissociated so as to control the concentration of oxygen in the gas diffusing into the second passage to as low a level as possible. Residual NO and O2 contained in the gas which has diffused into the second passage are dissociated. The concentration of NOx in the measurement gas is obtained based on a first pumping current, which is induced by oxygen ions generated by the dissociation of O2 and NO within the first passage, and a second pumping current, which is induced by oxygen ions generated by the dissociation of NO and O2 within the second passage. According to a second mode of the fifth aspect of the invention, the concentration of NOx in the measurement gas is obtained based on the NO dissociation percentage in the first passage. According to a third mode of the fifth aspect of the invention, the concentration of NOx in the measurement gas is obtained based on the NO dissociation percentage in the first passage and the rate of variation in NO concentration due to control of the concentration of oxygen in the gas diffusing into the second passage causing a variation in the ratio between the concentration of NO in the measurement gas and the concentration of NO in the gas diffusing into the second passage. According to a fourth mode of the fifth aspect of the invention, the NO dissociation percentage in the first passage is corrected for the concentration of oxygen in the measurement gas.
A first mode of a sixth aspect of the present invention provides an apparatus for measuring NOx concentration, comprising a first passage, a second passage, an oxygen-concentration-measuring cell, a first pumping cell, a second pumping cell, first pumping cell control means and second pumping cell control means. A measurement gas diffuses into the first passage via a first diffusion resistance element. In the first passage, O2 and NO partially dissociate. The gas leaving the first passage diffuses into the second passage via a second diffusion resistance element facing a downstream end portion of the first passage. In the second passage, residual NO and O2 contained in the gas dissociate. The oxygen-concentration-measuring cell has an electrode which is disposed downstream of the first passage and in the vicinity of an inlet to or facing the second diffusion resistance element. The oxygen-concentration-measuring cell outputs an electromotive force by means of a concentration cell effect and according to the concentration of oxygen in the gas contacting the oxygen-concentration-measuring cell. By applying a voltage to the first pumping cell based on the electromotive force output from the oxygen-concentration-measuring cell, the first pumping cell causes a portion of O2 and NO in the first passage to dissociate. A first pumping current induced by oxygen ions generated by the dissociation of O2 and NO flows through the first pumping cell. By applying a voltage to the second pumping cell, the second pumping cell causes residual O2 and NO in gas which has diffused into the second passage to dissociate. A second pumping current induced by oxygen ions generated by the dissociation of residual O2 and NO flows through the second pumping cell. The first pumping cell control means applies a voltage to the first pumping cell such that a portion of O2 and NO in the first passage dissociates. This controls the concentration of oxygen contained in the gas diffusing into the second passage to as low a level as possible. The second pumping cell control means applies a voltage to the second pumping cell such that residual NO and O2 in gas which has diffused into the second passage dissociates. According to a second mode of the sixth aspect of the invention, the apparatus of the first mode of the sixth aspect of the invention further comprises means for storing the relationship between oxygen concentration and gain for NO concentration; and means for solving a relational expression between the first pumping current and oxygen concentration which includes a term whose value varies with NO concentration, as well as a relational expression between the second pumping current and NO concentration which includes a term whose value varies with oxygen concentration, based on the measured first pumping current, the measured second pumping current and the stored relationship between oxygen concentration and gain for NO concentration.
A seventh aspect of the present invention provides a method for measuring the concentration of a certain gas component contained in a measurement gas, comprising the steps of: measuring an oxygen ion pump current which flows when an oxygen ion pump means is operated so as to dissociate a portion of the certain gas component in a measurement gas which has been introduced into a passage; measuring an oxygen ion pump current which flows when the oxygen ion pump means is operated so as to dissociate the residual certain gas component in the gas which has undergone dissociation of a portion of the certain gas component; and determining the concentration of the certain gas component in the measurement gas based on the two measured oxygen ion pump currents.
An eighth aspect of the present invention provides an apparatus for measuring the concentration of a certain gas component in a measurement gas, comprising: oxygen ion pump means faces a passage into which the measurement gas is introduced and whose operation for pumping out oxygen from the passage causes a pump current to flow; means for measuring an oxygen ion pump current which flows when the oxygen ion pump means is operated so as to dissociate a portion of the certain gas component in the measurement gas that has been introduced into the passage; means for measuring an oxygen ion pump current which flows when the oxygen ion pump means is operated so as to dissociate the residual certain gas component contained in the gas in which a portion of the certain gas component has been dissociated; and means for determining the concentration of the certain gas component in the measurement gas based on the two measured oxygen ion pump currents. In the seventh and eight aspects of the invention, the certain gas component is preferably NOx.
In the above-described aspects of the present invention (particularly the third through sixth aspects), oxygen concentration in the first passage is controlled to as low a level as possible so long as a portion of the NO contained in the measurement gas dissociates in the first passage. This decreases the concentration of oxygen in gas diffusing into the second passage to as low a level as possible, thereby decreasing the oxygen concentration dependence and temperature dependence of the NOx concentration measurement. Residual NO is dissociated in the second passage. Based on current which is generated by the dissociation of residual NO, the NOx concentration is calculated taking into account the NO dissociation percentage in the first passage. Thus, the concentration of NOx in the measurement gas can be obtained very accurately.
A first mode of a ninth aspect of the present invention provides a method for measuring the concentration of NOx in a measurement gas using an NOx concentration sensor having at least two spaces into which the measurement gas is introduced. The method comprises the steps of: introducing the measurement gas into at least a first space and causing dissociation of a portion of NO and O2 in the first space; introducing the gas from the first space into a second space and causing dissociation of residual NO and O2 in the second space; and determining the concentration of NOx in the measurement gas based on the quantity of NO and O2 dissociated in the first and second spaces.
According to a second mode of the ninth aspect of the invention, the concentration of NOx in the measurement gas is obtained according to the following equations:
xcex1=f(Ip1),
xcex2=g(Ip1),
and
(1xe2x88x92xcex1/100)xc3x97(NOx concentration)+xcex2=Ip2,
where
xcex1: NO dissociation percentage in the first space (%),
xcex2: offset component of second pumping current corresponding to the quantity of oxygen dissociated in the second space,
NOx concentration: concentration of NOx in the measurement gas,
Ip1: first pumping current flowing through the first pumping cell,
Ip2: second pumping current flowing through the second pumping cell,
f: symbol expressing a functional relationship between xcex1 and Ip1, and
g: symbol expressing a functional relationship between xcex2 and Ip1.
In order to establish the correlation between the unit quantity of Ip2 and that of NOx concentration, the right-hand member of the above third expression may be multiplied by coefficient A. Notably, Ip2 may be adjusted in order to establish the correlation between the unit quantity of Ip2 and that of NOx concentration. The functions f and g can be experimentally obtained. In a simple method, xcex1 and xcex2 can be obtained from Ip1 using a map.
According to a third mode of the ninth aspect of the invention, by using a previously prepared three-dimensional map showing the relationship among the first pumping current, the second pumping current and the concentration of NOx in the measurement gas, the concentration of NOx in the measurement gas is obtained based on a measured first pumping current and a measured second pumping current.
The present invention will next be described with reference to the drawings, while using, as an example, an NOx concentration sensor in which a measurement gas is diffused into a first internal passage; oxygen is pumped out by means of a first pumping cell from the first passage; gas having a controlled oxygen concentration is diffused into a second passage from the first passage; and a second pumping cell which causes NOx in the gas to dissociate. The drawings are referenced for explanation, and should not be construed as limiting the invention. In the description below, NOx concentration=(gain for NOx concentration)xc3x97(variation in output from NOx concentration sensor). Notably, in the present invention, the NOx concentration gain is the variation in NOx concentration corresponding to a constant variation in sensor output (ppm/xcexcA), namely, the reciprocal of sensor sensitivity.
First, the partial dissociation of NO in the first passage will be described. As shown in FIG. 14, an electrode 6b of a first pumping cell 6 is formed along the direction of measurement gas flow. The first pumping cell 6 undergoes feedback control based on an output from an oxygen concentration detection electrode 7a. As gas introduced into a first passage 2 diffuses, oxygen contained in the gas is gradually pumped out. Consequently, the oxygen concentration in the first passage 2 gradually decreases toward the downstream end of the first passage 2. The oxygen concentration detection electrode 7a detects an average oxygen concentration in a local space which faces the electrode 7a. That is, the oxygen concentration detection electrode 7a detects and outputs a local oxygen concentration in the vicinity of the center of the electrode 7a. Accordingly, the first pumping cell 6 substantially controls the oxygen concentration in the gas diffusing into a second passage such that the local oxygen concentration detected in the vicinity of the center of the oxygen concentration detection electrode 7a assumes a target oxygen concentration. As a result, the oxygen concentration of the local space in the vicinity of the center of the oxygen concentration detection electrode 7a agrees with the target oxygen concentration, whereas the oxygen concentration of the space located downstream of the central portion of the electrode 7a is lower than the target oxygen concentration. In the local space of lower oxygen concentration NO is more likely to dissociate, as seen from the formula xe2x80x9c2NOxe2x86x92N2+O2xe2x80x9d.
The concentration of oxygen in the gas diffusing into the second passage is controlled so as to become constant regardless of the concentration of oxygen in the measurement gas. Accordingly, the oxygen concentration gradient in the first passage 2 becomes steeper in the case of a high oxygen content in the measurement gas than that in the case of a measurement gas having a low oxygen content. As a result, a local space having a low oxygen concentration emerges within the first passage 2. Thus, the NO dissociation percentage in the first passage 2 varies according to the concentration of oxygen in the measurement gas.
First, based on the assumption that NO does not dissociate in the first passage, a theoretical expression for NOx concentration gain will be described. When the measurement gas is introduced into the NOx concentration sensor, the composition of gas diffusing into the second passage gradually varies and reaches a steady state. This is illustrated in FIG. 15. FIG. 16 shows a process of obtaining a gain for NOx concentration in the manner of a geometrical series in the case of FIG. 15.
As shown in FIGS. 15 and 16, a measurement gas which contains oxygen in a proportion of a and NO in a proportion of b is introduced into the NOx concentration sensor. Oxygen is pumped out from the first passage such that the concentration of oxygen in gas diffusing into the second passage approaches 0%. As a result, the measurement gas diffuses into the first passage at the same rate as that of the pumped-out oxygen. Thus, the gas diffusing into the second passage contains NO in a proportion of xe2x80x9ca+abxe2x80x9d (steps 101 and 102). The step of pumping out oxygen is repeated until the concentration of oxygen in the gas diffusing into the second passage reaches a target value (step 103). As a result of repeating steps 101 and 102, finally, the proportion of NO contained in the gas diffusing into the second passage becomes b/(1xe2x88x92a) (step 104). Because the NO gain is proportional to the reciprocal of the proportion of NO in the gas diffusing into the second passage, the theoretical expression xe2x80x9cNO gain [theoretical value]=gain0xc3x97{1xe2x88x92O2[%]/100}xe2x80x9d is deduced (step 105). As seen from the theoretical expression, the NO gain varies with the concentration of oxygen in the measurement gas.
Next, a theoretical expression for NO gain in the case where NO dissociates in the first passage will be described with reference to FIG. 17. Oxygen is pumped out from the first passage, and NO dissociates in the first passage (step 201). Thus, with bxe2x80x2=b{1xe2x88x92(NO dissociation percentage [%] in first passage)/100}, the proportion of NO contained in the gas diffusing into the second passage is represented by xe2x80x9cbxe2x80x2+abxe2x80x2xe2x80x9d. As a result of repeating steps 201 and 202, finally, the proportion of NO in the gas diffusing into the second passage becomes bxe2x80x2/(1xe2x88x92a) (steps 203 and 204). Thus, the theoretical expression xe2x80x9cNO gainxe2x80x9d=gain0/{1xe2x88x92(NO dissociation percentage [%] in first passage)/100}xc3x97{1xe2x88x92O2[%]/100)} is deduced (step 205). As seen from the theoretical expression, the NO gain also varies with the NO dissociation percentage in the first passage.
As seen from the theoretical expressions obtained in steps 105 and 205, the NO gain [no dissociation] in the case where No does not dissociate in the first passage and the NO gain [dissociation] in the case where NO dissociates in the first passage have the following relationship: NO gain [dissociation]=NO gain [no dissociation]/{1xe2x88x92(NO dissociation percentage [%] in the first passage)/100}. Thus, based on the NO dissociation percentage in the first passage at a certain measurement gas oxygen concentration and the NO gain [no dissociation] at that oxygen concentration, the NO gain [dissociation] at a certain measurement gas oxygen concentration is obtained.
Next, a preferred embodiment of the present invention will be described. Specifically, a method for measuring NOx concentration using an NOx concentration sensor as shown in FIGS. 18 and 19 will be described. FIG. 20 shows where the plane of FIGS. 18 and 19 is located within a sensor element. The NOx concentration sensor of FIGS. 18 and 19 has a first pumping cell 6, an oxygen-concentration-measuring cell 7 and a second pumping cell 8 arranged in layers. A first passage 2 is provided so as to face the first pumping cell 6 and the oxygen-concentration-measuring cell 7. A second passage 4 is provided so as to face the second pumping cell 8. A first porous diffusion hole (resistance element) 1 is provided at an inlet to the first passage 2. A second porous diffusion hole (resistance element) 3 is provided at an inlet to the second passage 4. The first and second pumping cells 6 and 8, respectively, are each composed of an oxygen-ion conductive solid electrolyte layer and a pair of electrodes formed on the solid electrolyte layer. The oxygen-concentration-measuring cell 7 is an oxygen concentration cell for generating an electromotive force Vsm by means of a concentration cell effect (hereinafter simply referred to as electromotive Vsm) depending on the concentration of oxygen (partial pressure of oxygen) in the gas diffusing into the second passage 4.
External circuits serving as control mean 20 and 21 are connected to the NOx concentration sensor in order to control the first and second pumping cells 6 and 8, respectively. Electrodes 6b and 7a are electrically connected, and their point of connection is grounded via a resistance. The electrode 7b is electrically connected to the inverted input terminal (xe2x88x92) of a differential amplifier 20a. A reference voltage Vs is input to the uninverted input terminal (+) of the differential amplifier 20a. In order to control the concentration of oxygen in the gas diffusing into the second passage 4 to a target value corresponding to the reference voltage Vs, the output the differential amplifier 20a reversibly controls a first pumping current Ip1. Thus, the first pumping current Ip1 flows between the electrodes 6a and 6b such that the electromotive force Vsm generated between the electrodes 7a and 7b assumes the reference voltage Vs. As a result, oxygen is pumped out from or pumped into the first passage 2. Meanwhile, a constant voltage Vp2 is applied between electrodes 8a and 8b, causing a second pumping current Ip2 to flow between the electrodes 8a and 8b. Reference oxygen generation means 22 supplies a small current between the electrodes 7a and 7b so as to pump out oxygen toward the electrode 7b side, thereby forming a reference oxygen space around the electrode 7b. In order to operate the NOx concentration sensor at an appropriate temperature, one or more unillustrated heaters are provided on or attached to a single side or opposite sides of a sensor element.
Control by First Pumping Cell Control Means 20
The reference voltage Vs is set, which is a target value of control for the electromotive force Vsm generated between the electrodes 7a and 7b of the oxygen-concentration-measuring cell 7. However, Vs is set such that a portion of NO and O2 in the first passage 2 dissociates so as to decrease the concentration of oxygen in the gas diffusing into the second passage 4 to as low a level as possible. As a result, an offset Ip2offset of the second pumping current Ip2 can be decreased as much as possible. Ip2offset, which is described below, is a value corresponding to the concentration of oxygen contained in the gas diffusing into the second passage 4, and hereinafter may be referred to as Ip20.
The first pumping cell 6 is subjected to feedback control such that the electromotive force Vsm becomes equal to the reference voltage Vs.
Control by Second Pumping Cell Control Means 21
The voltage Vp2 is applied between the electrodes 8a and 8b of the second pumping cell 8 such that all of the NO diffusing into the second passage 4 dissociates.
According to a preferred embodiment of the method for measuring NOx of the present invention, while the concentration of oxygen in the measurement gas is varied, the first pumping current and the NO dissociation percentage are measured. The thus-measured relationship is stored in the form of a map or a relational expression in, for example, a memory provided in the NOx concentration sensor. During operation of the sensor, the first pumping current is periodically measured, and an NO dissociation percentage is calculated which corresponds to an oxygen concentration at the measured first pumping current.
Other factors which would otherwise influence the measurement of NOx concentration can be compensated for by experimentally obtaining a coefficient for xcex94Ip2 in advance, to thereby obtain sufficient measurement accuracy.
The preferred embodiment of the method for measuring NOx concentration of the present invention takes into account both the dissociation of NO and an increase in NOx concentration caused by pumping out oxygen from the first passage. This preferred embodiment will next be described in detail.
A measurement gas including NO and oxygen diffuses into the first passage 2.
As the measurement gas diffuses within the first passage 2, O2 contained in the gas dissociates, particularly above the electrode 6b. Oxygen ions generated by the dissociation of O2 are pumped out toward the electrode 6 a side; consequently, oxygen concentration in the first passage 2 decreases (see FIG. 14). Also, a portion of the NO dissociates in the first passage 2. Oxygen ions generated by the dissociation of O2 and by the dissociation of NO cause a first pumping current Ip1 to flow between the electrodes 6a and 6b of the first pumping cell 6, to which the voltage Vp1 is applied. As the concentration of oxygen in the measurement gas with respect to a target oxygen concentration corresponding to Vs increases, the NO concentration in the first passage 2 increases because more oxygen is pumped out from the first passage 2. Thus, as the concentration of oxygen in the measurement gas increases, the concentration of NO contained in the gas diffusing into the second passage 4 increases.
Oxygen concentration is sufficiently decreased by action of the first pumping cell, and a gas which contains residual NO diffuses into the second passage 4.
Residual O2 and NO contained in the gas which has diffused into the second passage 4 dissociate. Oxygen ions generated by the dissociation of O2 and by the dissociation of NO cause a second pumping current Ip2 to flow between the electrodes 8a and 8b of the second pumping cell 8, to which a the constant voltage Vp2 is applied.
The reason for causing a portion of NO in the first passage to dissociate will next be described. In order to the decrease oxygen concentration dependence and temperature dependence of the NOx concentration measurement so as to provide a high degree of measurement accuracy, the concentration of oxygen in the gas diffusing into the second passage must be considerably decreased. To this end, in the present invention, oxygen is sufficiently pumped out from the first passage such that a portion of NO in the first passage dissociates. By performing such oxygen concentration control in the vicinity of the second porous diffusion hole, a region having an oxygen concentration lower than a target oxygen concentration emerges in the first passage. In this region, the dissociation of NO is particularly accelerated.
The calculation of NOx concentration based on the first and second pumping currents Ip1 and Ip2, respectively, will next be described. The method for calculating NOx concentration will be schematically described using a number-of-molecules model. First, it is assumed that NO does not dissociate in the first passage. Here, the measurement gas (the total number of molecules per unit volume=10,000) has the following composition: the number of NO molecules=10; the number of O2 molecules=1,000; and the number of N2 molecules=8,990. When the number of O2 molecules in the gas diffusing into the second passage is taken as 1, the number of NO molecules in the gas diffusing into the second passage is calculated as 10xc3x979,999/9,000 at steady state. Next is the case where the measurement gas has the following composition: the number of NO molecules=10; the number of O2 molecules=100; and the number of N2 molecules=9,890. When the number of O2 molecules in the gas diffusing into the second passage is taken as 1, the number of NO molecules in the gas diffusing into the second passage is calculated as 10xc3x979,999/9,900 at steady state. Because the number of NO molecules=(gain for the number of NO molecules)xc3x97(the number of NO molecules (in the gas which has diffused into the second passage)), as the concentration of oxygen in the measurement gas increases, the gain for the number of NO molecules decreases.
Next is the case where NO dissociates in the first passage. Here, the measurement gas (the total number of molecules per unit volume=10,000) has the following composition: the number of NO molecules=10; the number of O2 molecules=1,000;and the number of N2 molecules=8,990. When one NO molecule dissociates (percentage of dissociation=10%, or ratio dissociation=0.1) in the first passage, and consequently the gas diffusing into the second passage contains one O2 molecule, the number of NO molecules in the gas diffusing into the second passage is obtained as 9xc3x979,999/9,000. This indicates that NO gain also varies as a result of the dissociation of NO in the first passage. Thus, the number of NO molecules can be obtained based on the concentration of oxygen (degree of enrichment of NO) in the measurement gas and the NO dissociation percentage in the first passage. Expressions for obtaining the concentration of NOx in the measurement gas based on Ip1 and Ip2 are shown below.                               Numbers          ⁢                      xe2x80x83                    ⁢          of          ⁢                      xe2x80x83                    ⁢          NO          ⁢                      xe2x80x83                    ⁢                      molecules            ⁢                          xe2x80x83                        [                          2              ⁢              st                        ]                          =                                                                                                                                                {                                                                              (                                                          number                              ⁢                                                              xe2x80x83                                                            ⁢                              of                              ⁢                                                              xe2x80x83                                                            ⁢                              NO                              ⁢                                                              xe2x80x83                                                            ⁢                                                              molecules                                ⁢                                                                  xe2x80x83                                                                [                                m                                ]                                                                                      )                                                    -                                                                                                                                                                                                  (                                                      number                            ⁢                                                          xe2x80x83                                                        ⁢                            of                            ⁢                                                          xe2x80x83                                                        ⁢                            NO                            ⁢                                                          xe2x80x83                                                        ⁢                                                          molecules                              ⁢                                                              xe2x80x83                                                            [                              d                              ]                                                                                )                                                }                                                                                                                                                                                                                                                              (                                                      total                            ⁢                                                          xe2x80x83                                                        ⁢                            number                            ⁢                                                          xe2x80x83                                                        ⁢                            of                            ⁢                                                          xe2x80x83                                                        ⁢                            molecules                                                    )                                                -                                                                                                                                                (                                                  number                          ⁢                                                      xe2x80x83                                                    ⁢                          of                          ⁢                                                      xe2x80x83                                                    ⁢                          oxygen                          ⁢                                                      xe2x80x83                                                    ⁢                                                      molecules                            ⁢                                                          xe2x80x83                                                        [                                                          2                              ⁢                              st                                                        ]                                                                          )                                                                                                                                                                                                          (                                          total                      ⁢                                              xe2x80x83                                            ⁢                      number                      ⁢                                              xe2x80x83                                            ⁢                      of                      ⁢                                              xe2x80x83                                            ⁢                      molecules                                        )                                    -                                                                                                      (                                      number                    ⁢                                          xe2x80x83                                        ⁢                    of                    ⁢                                          xe2x80x83                                        ⁢                    oxygen                    ⁢                                          xe2x80x83                                        ⁢                                          molecules                      ⁢                                              xe2x80x83                                            [                      m                      ]                                                        )                                                                                        (        a        )            
where
[m]: within measurement gas,
[2st]: within gas which has diffused into the second passage, and number of NO molecules [d]: number of NO molecules dissociated in the first passage.
Here,             Enrichment      ⁢              xe2x80x83            ⁢      percentage        =                                                                                        (                                      total                    ⁢                                          xe2x80x83                                        ⁢                    number                    ⁢                                          xe2x80x83                                        ⁢                    of                    ⁢                                          xe2x80x83                                        ⁢                    molecules                                    )                                -                                                                                        (                                  number                  ⁢                                      xe2x80x83                                    ⁢                  of                  ⁢                                      xe2x80x83                                    ⁢                  oxygen                  ⁢                                      xe2x80x83                                    ⁢                                      molecules                    ⁢                                          xe2x80x83                                        [                                          2                      ⁢                      st                                        ]                                                  )                                                                                                                          (                                      total                    ⁢                                          xe2x80x83                                        ⁢                    number                    ⁢                                          xe2x80x83                                        ⁢                    of                    ⁢                                          xe2x80x83                                        ⁢                    molecules                                    )                                -                                                                                        (                                  number                  ⁢                                      xe2x80x83                                    ⁢                  of                  ⁢                                      xe2x80x83                                    ⁢                  oxygen                  ⁢                                      xe2x80x83                                    ⁢                                      molecules                    ⁢                                          xe2x80x83                                        [                    m                    ]                                                  )                                                        xc3x97      100      ⁢              (        %        )                        Dissociation      ⁢              xe2x80x83            ⁢      percentage        =                            (                      number            ⁢                          xe2x80x83                        ⁢            of            ⁢                          xe2x80x83                        ⁢            NO            ⁢                          xe2x80x83                        ⁢                          molecules              ⁢                              xe2x80x83                            [              d              ]                                )                          (                      number            ⁢                          xe2x80x83                        ⁢            of            ⁢                          xe2x80x83                        ⁢            NO            ⁢                          xe2x80x83                        ⁢                          molecules              ⁢                              xe2x80x83                            [              m              ]                                )                    xc3x97      100      ⁢              (        %        )            
Substituting them into Expression (a) gives                               Number          ⁢                      xe2x80x83                    ⁢          of          ⁢                      xe2x80x83                    ⁢          NO          ⁢                      xe2x80x83                    ⁢                      molecules            ⁢                          xe2x80x83                        [                          2              ⁢              st                        ]                          =                  xe2x80x83                ⁢                  {                                    (                              number                ⁢                                  xe2x80x83                                ⁢                of                ⁢                                  xe2x80x83                                ⁢                NO                ⁢                                  xe2x80x83                                ⁢                                  molecules                  ⁢                                      xe2x80x83                                    [                  m                  ]                                            )                        -                                                                        xe2x80x83                    ⁢                      (                          number              ⁢                              xe2x80x83                            ⁢              of              ⁢                              xe2x80x83                            ⁢              NO              ⁢                              xe2x80x83                            ⁢                              molecules                ⁢                                  xe2x80x83                                [                d                ]                                      )                    }                xc3x97                                          xe2x80x83                ⁢                              (                          enrichment              ⁢                              xe2x80x83                            ⁢              percentage                        )                    /          100                                        =                  xe2x80x83                ⁢                              {                          1              -                                                (                                      dissociation                    ⁢                                          xe2x80x83                                        ⁢                    percentage                                    )                                /                100                                      }                    xc3x97                                                  xe2x80x83                ⁢                              (                          number              ⁢                              xe2x80x83                            ⁢              of              ⁢                              xe2x80x83                            ⁢              NO              ⁢                              xe2x80x83                            ⁢                              molecules                ⁢                                  xe2x80x83                                [                m                ]                                      )                    xc3x97                                                  xe2x80x83                ⁢                              (                          enrichment              ⁢                              xe2x80x83                            ⁢              percentage                        )                    /          100                    
Rearrangement gives                               Number          ⁢                      xe2x80x83                    ⁢          of          ⁢                      xe2x80x83                    ⁢          NO          ⁢                      xe2x80x83                    ⁢                      molecules            ⁢                          xe2x80x83                        [            m            ]                          =                              (                          number              ⁢                              xe2x80x83                            ⁢              of              ⁢                              xe2x80x83                            ⁢              NO              ⁢                              xe2x80x83                            ⁢                              molecules                ⁢                                  xe2x80x83                                [                                  2                  ⁢                  st                                ]                                      )                                                                                                    {                                          1                      -                                                                        (                                                      dissociation                            ⁢                                                          xe2x80x83                                                        ⁢                            percentage                                                    )                                                /                        100                                                              }                                    xc3x97                                                                                                                          (                                          enrichment                      ⁢                                              xe2x80x83                                            ⁢                      percentage                                        )                                    /                  100                                                                                        (        b        )            
Assuming that the number of oxygen atoms and a unit current make a one-by-one correspondence,
Ip2=(number of NO molecules [2st])+2xc3x97(number of oxygen molecules [2st])
then
Ip2={1xe2x88x92(dissociation percentage)/100}xc3x97(enrichment percentage)/100xc3x97(number of NO molecules [m])+2xc3x97(number of oxygen molecules [2st]xe2x80x83xe2x80x83(c)
                              Number          ⁢                      xe2x80x83                    ⁢          of          ⁢                      xe2x80x83                    ⁢          NO          ⁢                      xe2x80x83                    ⁢                      molecules            ⁢                          xe2x80x83                        [            m            ]                          =                              Ip2            -                          2              xc3x97                              (                                  number                  ⁢                                      xe2x80x83                                    ⁢                  of                  ⁢                                      xe2x80x83                                    ⁢                  oxygen                  ⁢                                      xe2x80x83                                    ⁢                                      molecules                    ⁢                                          xe2x80x83                                        [                                          2                      ⁢                      st                                        ]                                                                                                                                                                {                                          1                      -                                                                        (                                                      dissociation                            ⁢                                                          xe2x80x83                                                        ⁢                            percentage                                                    )                                                /                        100                                                              }                                    xc3x97                                                                                                                          (                                          enrichment                      ⁢                                              xe2x80x83                                            ⁢                      percentage                                        )                                    /                  100                                                                                        (        d        )            
Taking xe2x80x9cnumber of NO molecules [m]=(gain for number of NO molecules)xc3x97xcex94Ip2xe2x80x9d gives                               Gain          ⁢                      xe2x80x83                    ⁢          for          ⁢                      xe2x80x83                    ⁢          number          ⁢                      xe2x80x83                    ⁢          of          ⁢                      xe2x80x83                    ⁢          NO          ⁢                      xe2x80x83                    ⁢          molecules                =                  1                                                                                          {                                          1                      -                                                                        (                                                      dissociation                            ⁢                                                          xe2x80x83                                                        ⁢                            percentage                                                    )                                                /                        100                                                              }                                    xc3x97                                                                                                                          (                                          enrichment                      ⁢                                              xe2x80x83                                            ⁢                      percentage                                        )                                    /                  100                                                                                        (        e        )            
Because the enrichment percentage is identical for the same oxygen concentration, the following expression is obtained for any oxygen concentration.                               1          -                                    (                              dissociation                ⁢                                  xe2x80x83                                ⁢                percentage                            )                        /            100                          =                                                                              (                                      NO                    ⁢                                          xe2x80x83                                        ⁢                    gain                    ⁢                                          xe2x80x83                                        ⁢                    under                    ⁢                                          xe2x80x83                                        ⁢                    the                    ⁢                                          xe2x80x83                                        ⁢                    condition                    ⁢                                          xe2x80x83                                        ⁢                    that                    ⁢                                          xe2x80x83                                        ⁢                    NO                                                                                                                                            does                    ⁢                                          xe2x80x83                                        ⁢                    not                    ⁢                                          xe2x80x83                                        ⁢                    dissociate                    ⁢                                          xe2x80x83                                        ⁢                    in                    ⁢                                          xe2x80x83                                        ⁢                    the                    ⁢                                          xe2x80x83                                        ⁢                    first                    ⁢                                          xe2x80x83                                        ⁢                    passage                                    )                                                                                                                          (                                      NO                    ⁢                                          xe2x80x83                                        ⁢                    gain                    ⁢                                          xe2x80x83                                        ⁢                    under                    ⁢                                          xe2x80x83                                        ⁢                    the                    ⁢                                          xe2x80x83                                        ⁢                    condition                    ⁢                                          xe2x80x83                                        ⁢                    that                    ⁢                                          xe2x80x83                                        ⁢                    NO                                                                                                                                            dissociates                    ⁢                                          xe2x80x83                                        ⁢                    in                    ⁢                                          xe2x80x83                                        ⁢                    the                    ⁢                                          xe2x80x83                                        ⁢                    first                    ⁢                                          xe2x80x83                                        ⁢                    passage                                    )                                                                                        (        f        )                                                                    Ip1              =                              xe2x80x83                            ⁢                              2                xc3x97                                  {                                                            (                                              number                        ⁢                                                  xe2x80x83                                                ⁢                        of                        ⁢                                                  xe2x80x83                                                ⁢                        oxygen                        ⁢                                                  xe2x80x83                                                ⁢                                                  molecules                          ⁢                                                      xe2x80x83                                                    [                          m                          ]                                                                    )                                        -                                                                                                                                                            xe2x80x83                                ⁢                                  (                                      number                    ⁢                                          xe2x80x83                                        ⁢                    of                    ⁢                                          xe2x80x83                                        ⁢                    oxygen                    ⁢                                          xe2x80x83                                        ⁢                                          molecules                      ⁢                                              xe2x80x83                                            [                                              2                        ⁢                        st                                            ]                                                        )                                }                            +                                                                                          xe2x80x83                            ⁢                              (                                  number                  ⁢                                      xe2x80x83                                    ⁢                  of                  ⁢                                      xe2x80x83                                    ⁢                  NO                  ⁢                                      xe2x80x83                                    ⁢                                      molecules                    ⁢                                          xe2x80x83                                        [                    d                    ]                                                  )                                                                                        =                              xe2x80x83                            ⁢                              2                xc3x97                                  {                                                            (                                              number                        ⁢                                                  xe2x80x83                                                ⁢                        of                        ⁢                                                  xe2x80x83                                                ⁢                        oxygen                        ⁢                                                  xe2x80x83                                                ⁢                                                  molecules                          ⁢                                                      xe2x80x83                                                    [                          m                          ]                                                                    )                                        -                                                                                                                                                            xe2x80x83                                ⁢                                  (                                      number                    ⁢                                          xe2x80x83                                        ⁢                    of                    ⁢                                          xe2x80x83                                        ⁢                    oxygen                    ⁢                                          xe2x80x83                                        ⁢                                          molecules                      ⁢                                              xe2x80x83                                            [                                              2                        ⁢                        st                                            ]                                                        )                                }                            +                                                                                          xe2x80x83                            ⁢                                                                    (                                          dissociation                      ⁢                                              xe2x80x83                                            ⁢                      percentage                                        )                                    /                  100                                xc3x97                                                                                                        xe2x80x83                            ⁢                                                (                                      number                    ⁢                                          xe2x80x83                                        ⁢                    of                    ⁢                                          xe2x80x83                                        ⁢                    NO                    ⁢                                          xe2x80x83                                        ⁢                    molecules                                    )                                ⁢                                  xe2x80x83                                [                m                ]                                                                        (        g        )            
Because the number of NO molecules per unit volume is the NOx concentration, the NOx concentration can be calculated based on the NO dissociation percentage in the first passage, the concentration of oxygen in the measurement gas, and the first and second pumping currents. Expressions for obtaining NOx concentration are shown below.                                                                         NO                ⁢                                  xe2x80x83                                ⁢                concentration                            =                              K                xc3x97                Δ                ⁢                                  xe2x80x83                                ⁢                Ip2                                                                                        =                              K                xc3x97                                  (                                      Ip2                    -                                          Ip2                      0                                                        )                                                                                        (        1        )            
where
K: gain for NO concentration (reciprocal of sensitivity), ppm/xcexcA, and
Ip20: offset of Ip2; Ip2 as measured when the concentration of NO in the measurement gas is 0 ppm.
K=K0+K1xc3x97O2[%]xe2x80x83xe2x80x83(2)
where
K0: gain for NO concentration when the concentration of oxygen in the measurement gas is 0%, and
K1: coefficient of an approximate expression representing the relationship between measured gain and oxygen concentration.
Substituting equation (2) into equation (1) gives:
NO concentration=(K0+K1xc3x97O2[%])xc3x97(Ip2xe2x88x92Ip20)xe2x80x83xe2x80x83(3)
The relationship between the NO dissociation percentage [%] and oxygen concentration [%] is represented by the following approximate expression:
NO dissociation percentage [%]=xcex10+K2xc3x97O2[%]+K3xc3x97O2[%]2xe2x80x83xe2x80x83(4)
where
NO dissociation percentage: (NO which has dissociated in first passage)/(NO contained in measurement gas)xc3x97100,
xcex10: NO dissociation percentage when the oxygen concentration is 0%, and
K2, K3: coefficients of an approximate equation representing the relationship between experimentally obtained NO dissociation percentage and oxygen concentration.
Oxygen concentration can be obtained by the following expression:                                                                                           O                  2                                ⁢                                  xe2x80x83                                [                %                ]                            =                              xe2x80x83                            ⁢                              K4                xc3x97                                  {                                      Ip1                    -                                          K5                      xc3x97                                              (                                                  NO                          ⁢                                                      xe2x80x83                                                    ⁢                          concentration                                                )                                            xc3x97                                                                                                                                                              xe2x80x83                            ⁢                                                                    (                                          NO                      ⁢                                              xe2x80x83                                            ⁢                      dissociation                      ⁢                                              xe2x80x83                                            ⁢                                              percentage                        ⁢                                                  xe2x80x83                                                [                        %                        ]                                                              )                                    /                  100                                -                                  Ip1                  0                                            }                                                                          =                              xe2x80x83                            ⁢                              K4                xc3x97                                  {                                      Ip1                    -                                          K5                      xc3x97                                              (                                                  NO                          ⁢                                                      xe2x80x83                                                    ⁢                          concentration                                                )                                            xc3x97                                                                                                                                                              xe2x80x83                            ⁢                                                                    (                                                                  α                        ⁢                                                  xe2x80x83                                                ⁢                        0                                            +                                              K2                        xc3x97                                                                              O                            2                                                    ⁢                                                      xe2x80x83                                                    [                          %                          ]                                                                    +                                              K3                        xc3x97                                                                                                            O                              2                                                        ⁢                                                          xe2x80x83                                                        [                            %                            ]                                                    2                                                                                      )                                    /                  100                                -                                  Ip1                  0                                            }                                                          (        5        )            
where
Ip10: Ip1 as measured when the concentration of NO in the measurement gas is 0 ppm and the oxygen concentration is 0%,
K4: coefficient of an approximate equation representing the relationship between oxygen concentration and xe2x80x9cIp1xe2x88x92Ip10xe2x80x9d obtained when the NO concentration is 0 ppm, and
K5: {current Ip1 (=IB) measured when NO of a predetermined concentration has all dissociated in the first passage}/(the predetermined NO concentration), i.e., current per an NO concentration of 1 ppm as measured when all the NO has dissociated in the first passage.
Proportional coefficients K0 through K5, Ip10 and Ip20 are experimentally obtained, and Ip1 and Ip2 are measured. Accordingly, NOx concentration and oxygen concentration can be obtained by solving the simultaneous system of equation (3) and equation (5).
A method for experimentally obtaining the proportional coefficients K0 through K5 will next be described.
K0
K0 is xe2x80x9cxcex94Ip2/xcex94NO concentrationxe2x80x9d obtained when the concentration of oxygen in the measurement gas is 0 ppm.
K1
While the concentration of oxygen in the measurement gas is varied, xe2x80x9cxcex94Ip2/xcex94NO concentrationxe2x80x9d is obtained. K1 is determined by solving an approximate expression representing the relationship between oxygen concentration and xe2x80x9cxcex94Ip2/xcex94NO concentrationxe2x80x9d.
K2 and K3
K2 and K3 are experimentally obtained from the relationship between the concentration of oxygen in the measurement gas and the NO dissociation percentage in the first passage. The NO dissociation percentage is obtained based on a limit current (=IB) of Ip1 as measured when all NO of a predetermined concentration dissociates in the first passage and xcex94Ip1 as measured under the condition that a portion of NO of the predetermined concentration dissociates in the first passage (xcex94Ip1=Ib =Ip1[NO=predetermined concentration]xe2x88x92Ip1[NO=0]). The NO dissociation percentage=Ib/IB
K4
K4 is a gain for oxygen concentration. Ip1 is measured for a measurement gas having an NO concentration of 0 ppm and an oxygen concentration of 0% and for a measurement gas having an NO concentration of 0 ppm and a predetermined oxygen concentration. K4 is experimentally obtained from the relationship between the change in oxygen concentration with the change in Ip1.
K5
K5 can be obtained based on IB described above, and the NOx concentration when Ip1 has reached IB. When the concentration of NOx in the measurement gas is very small as compared to the concentration of oxygen in the measurement gas, xe2x80x9cK5xc3x97(NO concentration)xc3x97(xcex10+K2xc3x97(oxygen concentration)+K3 xc3x97(oxygen concentration)2)xe2x80x9d in equation (5) may be substantially taken as 0. In this case, the concentration of oxygen in the measurement gas can be directly obtained from a measured Ip1.
Position of Oxygen Concentration Detection Electrode
As seen from FIGS. 14 and 21, when the concentration of oxygen in the measurement gas changes, the gradient of oxygen concentration within the first passage 2 changes, and the NO dissociation percentage in the first passage 2 changes. As shown in FIG. 14, by disposing the oxygen concentration detection electrode (Vs electrode) 7a in the vicinity of the inlet to the second diffusion hole 3, an error or difference between a target oxygen concentration (detected oxygen concentration) and the concentration of oxygen in the gas diffusing into the second passage 4 decreases, and thus the oxygen concentration dependence of offset (Ip20) decreases. By contrast, as shown in FIG. 21, when the Vs electrode 7a is disposed in the vicinity of the first diffusion hole 3, the above-mentioned error increases due to the influence of the oxygen concentration gradient in the first passage 2 and the influence of a variation in the concentration of oxygen in the measurement gas. Furthermore, when the concentration of oxygen in the measurement gas is high, the oxygen concentration gradient in the first passage 2 becomes steep. As a result, a region having an excessively low oxygen concentration expands within the first passage 2 as compared to the case of FIG. 14, causing an increase in the oxygen concentration dependence of the NO dissociation percentage. Accordingly, in order to decrease the oxygen concentration dependence of offset (Ip20) and the oxygen concentration dependence of the NO dissociation percentage, the Vs electrode 7a is preferably disposed in the vicinity of the inlet to the second porous diffusion element 3 so as to be disposed away from the first diffusion hole 3.